Wash and peel two medium-sized cucumbers, chop them into chunks, and set aside. Cut the lime into quarters and rinse mint leaves.

In a blender, combine chopped cucumber, lime quarters, mint, and lemongrass with four cups of filtered water. Blend on high for 30-40 seconds.

Using a fine mesh strainer, pour the blended mixture over a large bowl to separate the pulp from the liquid, pressing gently to extract juice.

Return the strained juice to the blender or pitcher, add sugar and honey to taste, and blend or stir until dissolved.

Chill the Cucumber Agua Fresca in the refrigerator for at least 30 minutes before serving over ice.